Determination of SLR Station Coordinates Based on LEO, LARES

Strugarek et al. Earth, Planets and Space (2021) 73:87 https://doi.org/10.1186/s40623-021-01397-1

FULL PAPER Open Access Determination of SLR station coordinates based on LEO, LARES, LAGEOS, and Galileo satellites Dariusz Strugarek1* , Krzysztof Sośnica1, Daniel Arnold2, Adrian Jäggi2, Radosław Zajdel1 and Grzegorz Bury1

Abstract The number of satellites equipped with retrorefectors dedicated to Satellite Laser Ranging (SLR) increases simultane- ously with the development and invention of the spherical geodetic satellites, low Earth orbiters (LEOs), Galileo and other components of the Global Navigational Satellite System (GNSS). SLR and GNSS techniques onboard LEO and GNSS satellites create the possibility of widening the use of SLR observations for deriving SLR station coordinates, which up to now have been typically based on spherical geodetic satellites. We determine SLR station coordinates based on integrated SLR observations to LEOs, spherical geodetic, and GNSS satellites orbiting the Earth at diferent altitudes, from 330 to 26,210 km. The combination of eight LEOs, LAGEOS-1/2, LARES, and 13 Galileo satellites increased the number of 7-day SLR solutions from 10–20% to even 50%. We discuss the issues of handling of range biases in multi-satellite combinations and the proper solution constraining and weighting. Weighted combination is characterized by a reduction of formal error medians of estimated station coordinates up to 50%, and the reduction of station coordinate residuals. The combination of all satellites with optimum weighting increases the consistency of station coordinates in terms of interquartile ranges by 10% of horizontal components for non-core stations w.r.t LAGEOS-only solutions. Keywords: Satellite Laser Ranging (SLR), GNSS, Low Earth orbiters (LEOs), Galileo, Reference frame realization

Introduction Hofmann et al. 2018), Very Long Baseline Interferom- Te International Association of Geodesy (IAG) estab- etry (VLBI; Schlüter and Behrend 2007), Global Naviga- lished services, which by using space geodetic tech- tion Satellite Systems (GNSS; Johnston et al. 2017), and niques, provide valuable infrastructure for observations Doppler Orbitography and Radiopositioning Integrated and products, used for description and understanding by Satellite (DORIS; Willis et al. 2010). Te IAG founded of the dynamic Earth system (Plag and Pearlman 2009). the Global Geodetic Observing System (GGOS; Plag and Four IAG services and their basic observation techniques Pearlman 2009; Gross et al. 2009) to provide the geodetic are used for deriving global geodetic parameters and expertise and infrastructure necessary for the monitoring the realization of the International Terrestrial Reference of the Earth system and global change research by inte- Frames (ITRF; Altamimi et al. 2016), including Satellite grating geodetic, geodynamic and geophysical commu- Laser Ranging (SLR; Pearlman et al. 2019a) and Lunar nities. Te GGOS requires 0.1 mm/year stable-in-time Laser Ranging (LLR, used in previous ITRF realizations; station velocities and the accuracy of 1 mm for the station coordinates. Te realization of the ITRF requires the *Correspondence: [email protected] position of geocenter (GCC), scale, and Earth orienta- 1 Institute of Geodesy and Geoinformatics, Wrocław University tion parameters determined with the accuracy of 1-mm of Environmental and Life Sciences, Grunwaldzka 53, 50‑357 Wrocław, Poland or better to appropriately realize the origin, metrics, and Full list of author information is available at the end of the article the orientation of the reference frame (Gross et al. 2009).

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Table 1 Characteristics of diferent types of satellites with SLR retrorefectors used in the analysis Satellite Type Main mission Launch date Altitude (km) Retrorefector POD techniques Attitude objective (mission end) characteristics information

LARES Spherical geo- Relativistic 02.2012 1450 Surface covered SLR – detic efects, gravity with 92 corner feld cubes LAGEOS-1 Spherical geo- ITRF, geocenter, 05.1976 10.1992 5850 5625 Surface covered SLR – LAGEOS-2 detic gravity feld, with 426 cor- ERPs ner cubes GRACE-A LEO Gravity feld, 03.2002 (10.2017) 450–330 Pyramid-shaped SLR, GNSS Quaternions, 5-s GRACE-B Ocean and Sea array,4 cubes interval monitoring SWARM-A LEO Earth Magnetic 11.2013 460 Pyramid-shaped SLR, GNSS Quaternions, 1-s SWARM-B feld, gravity 530 array,4 cubes interval SWARM-C feld 460 TerraSAR-X LEO Remote sensing 06.2007 514 Pyramid-shaped SLR, GNSS Quaternions, 10-s array,4 cubes interval Jason-2 LEO Ocean surface 06.2008 (10.2019) 1336 Hemispheri- SLR, GNSS, Quaternions, 30-s topography cal surface, 9 DORIS interval cubes Sentinel-3A LEO Ocean and land 02.2016 815 Spherical surface, SLR, GNSS, Quaternions, 1-s monitoring, 7 cubes DORIS interval ocean topography Galileo (3 IOV 10 GNSS Positioning, navi- IOV 10.2011 FOC 17 178– 23 222 Arrays of 84 SLR, GNSS Yaw-steering FOC) gation, timing 08.2014 cubes (IOV) and 60 cubes (FOC)

Tese requirements cannot be fulflled without a net- parameter GM, gravity feld parameters (Bloßfeld et al. work of high-quality observing, co-located GGOS sites, 2015; Sośnica et al. 2015a), and for the verifcation of gen- which provide the necessary infrastructure to detect eral relativity efects (Ciufolini et al. 1998). Te distribu- and reduce sources of systematic errors of observation tion of all normal points (NPs) collected by SLR stations systems, and to fully exploit the current constellation of in 2016–2018 reveals that in total 81% of all SLR observa- satellite missions. Nowadays, the combination of space tions were collected to LEOs, over 10% of the observa- geodetic techniques is based on co-located GGOS sites tions to GNSS satellites, and the remaining observations equipped with diferent techniques, however, the future comprising less than 9% of all SLR observations to spher- co-location onboard active satellites is foreseen, as well. ical geodetic satellites1. Only these latter were used so Co-location of space geodetic techniques onboard GNSS far for deriving global geodetic parameters, and for the satellites and active low Earth orbiters (LEOs) pave the computation of geodetic reference frames using the SLR way for new opportunities to future inter-technique con- technique. Te spacecraft and orbit characteristics of nections, for the ITRF realizations through the integra- diferent satellite types with the SLR retrorefectors are tion of various types of geodetic observation systems and summarized in Table 1 and Fig. 1. their products. SLR spherical geodetic satellites, such as LAGEOS-1/2 and LARES, are covered with corner cube retrorefectors, SLR observations to spherical geodetic, LEO, and GNSS with reduced area-to-mass ratios (Pearlman et al. 2019b). satellites Tose satellites are used to estimate geodetic parameters Te SLR technique employs optical range measurements because out of all artifcial satellites, their orbits are not to various types of satellites equipped with laser ret- very much afected by non-gravitational perturbations. rorefector arrays (LRA). Te main contribution of the Te mission main objectives include determining the ter- SLR technique to GGOS originates from measurements restrial reference frame and Earth rotation parameters to spherical geodetic satellites, such as LAGEOS-1/2, Etalon-1/2, which are used for the determination of GCC, global scale, station coordinates (Taller et al. 2011; Gla- 1 https://ilrs.cddis.eosdis.nasa.gov/network/system_performance/global_ ser et al. 2019; Zajdel et al. 2019), standard gravitational report_cards/ index. html . Strugarek et al. Earth, Planets and Space (2021) 73:87 Page 3 of 21

Fig. 1 Satellite missions equipped with various techniques onboard with their operation periods and altitudes

(ERPs) and improving the gravity feld models. Te main Te worldwide GNSS constellations are: the Ameri- objective of the LARES satellite are the measurement of can GPS, the Russian GLONASS, the European Galileo, relativistic efects, including the Lense–Tirring efect, and the Chinese BeiDou. Te Galileo system is expected space geodesy and geodynamics (Ciufolini et al. 2015). to complete constellation deployment in 2022. In terms SLR measurements to active LEOs, such as GRACE- of GNSS satellites, the SLR observations already proved A/B (Tapley et al. 2004), Sentinel-3A/B (Donlon et al. to be useful for the determination of the GNSS orbits 2012), and Jason-2 (Lambin et al. 2010), or GNSS con- using combined GNSS and SLR observations (Bury stellations are typically employed for the validation of et al. 2021). Te International GNSS Service (IGS; John- microwave-based or DORIS-based orbits of active LEOs, ston et al. 2017) initiated the Multi-GNSS Experiment and microwave-based orbits of GNSS satellites. Te (MGEX; Montenbruck et al. 2017) to track, collate, and number of active LEO satellites, which were equipped analyze all available GNSS signals for providing high- with at least two diferent positioning techniques, i.e., precision products accessible to a wide range of engi- SLR+GNSS, SLR+GNSS+DORIS, or SLR+DORIS has neering and science communities. All active Galileo been increasing for the last 20 years. Te co-location of satellites are equipped with LRA for SLR. Between 2014 SLR and GNSS can be found on satellites, such as GOCE and 2020 the International Laser Ranging Service (ILRS; (Drinkwater et al. 2007), GRACE-A/B, CHAMP (Reig- Pearlman et al. 2019a) initiated several intensive tracking ber et al. 2000), SWARM-A/B/C (Friis-Christensen et al. campaigns of GNSS in order to improve the scheduling, 2008), TerraSAR-X (Buckreuss et al. 2003), TanDEM-X increase the data volume especially in the daytime, and to (Krieger et al. 2007), Sentinel-3A/B, Sentinel-6/Jason- fnd the best possible tracking strategy (Bury et al. 2019). CS, and Jason-1/2/3. Depending on the mission require- Te Galileo constellation achieved partial operational ments and objectives, the LEOs have diferent shapes, capability in late 2018 with 24 active satellites. In this constructions, orbit characteristics, and specifc scientifc analysis, we use two types of Galileo satellites: In-Orbit instruments or payload onboard, such as GNSS receiv- Validation (IOV), launched in 2011, and Full Operational ers, accelerometers, communication devices, solar pan- Capability (FOC), launched in 2014–2018 (Steigenberger els, propulsion systems, and LRAs. Te LRAs onboard and Montenbruck 2017). Te IOV LRAs consist of 84 LEOs have either four cubes arranged on a regular 45° corner cubes, whereas FOC LRAs consist of 60 corner pyramid-shaped array, seven cubes arranged on a spheri- cubes, both types are arranged as fat panels2 (Table 1). cal surface, or eight corner cubes symmetrically mounted on a hemispherical surface with one nadir-looking cor- Determination of geodetic parameters based on SLR ner cube in the center (Table 1; Arnold et al. 2019). To observations to LEO and GNSS achieve the mission objectives, the requirements for Te realization of terrestrial reference frames based LEOs orbit accuracy reaches the level of 1–2 cm for on active LEO was previously studied by, e.g., Haines altimetry and gravity feld recovery missions (e.g., Sen- tinel-3, GRACE), thus the determined orbits must be of the superior accuracy. 2 http://ilrs. gsfc. nasa. gov/ docs/ retro refe ctor_ speci fcat ion_ 070416. pdf . Strugarek et al. Earth, Planets and Space (2021) 73:87 Page 4 of 21

et al. (2015), Männel and Rothacher (2017), Koenig Galileo constellation have been being developed since (2018), who focused on selected missions and the pos- the end of 2014. Tus, we conduct the analysis for the sibility of deriving origin, scale, and the orientation of 2016.0–2017.0 period. We derive the best combination the reference frames using LEO. SLR measurements strategy of SLR observations to passive and active satel- to single active LEO satellites were used by Guo et al. lites at diferent heights, from 330 to 26,200 km, diferent (2018) together with the GPS-based kinematic orbits of revolution periods, and equipped with diferent onboard GRACE-A for the determination of SLR station coordi- devices and LRA (Table 1, Fig. 1). nates in 2012. Te authors achieved a consistency at the We check whether SLR measurements to other than level of 20–30 mm, w.r.t. SLR-specifc ITRF2014 reali- spherical geodetic satellites either can be used as an alter- zation, SLRF2014. Couhert et al. (2018) used DORIS- native or as an enhancement of standard SLR solutions, only and SLR-only observations to Jason-2. Arnold et al. or whether they are insufcient for the determination of (2019) used SLR observations and GNSS-based orbits SLR station coordinates of better quality because of the of LEO satellites for the determination of corrections to systematic errors embedded in GNSS-based orbits and SLR station coordinates, range biases, and timing of- SLR measurements to non-spherical LRAs. We investi- sets and achieved 5–10 mm precision of SLR residuals. gate the quality of determined SLR station coordinates Strugarek et al. (2019a) combined SLR measurements to and the quantity of possible solutions. In the past, such Sentinel-3A/B and LAGEOS-1/2 and achieved a consist- an analysis was not possible because of the difculties ency of estimated station coordinates, characterized by in precise orbit determination (POD) of active satellites interquartile range, better than 13 mm and GCC with an equipped with large-size solar panels and resulting in RMS of 6 mm. Considering SLR to GNSS-only, and com- substantial non-gravitational forces perturbing the orbits. binations with spherical geodetic satellites, Taller et al. Modeling of precise orbits of heavy, spherical, geodetic (2011) combined SLR observations to GPS and GLO- satellites is much easier and hence has been employed for NASS satellites for the determination of the terrestrial the determination of geodetic parameters. In this study, reference frame, the GNSS satellite antenna ofsets, and we use state-of-the-art modeling strategies for LEO and the SLR range biases and achieved 1–2 cm agreement of GNSS orbits employing precise GNSS-based LEO and estimated station coordinates with a priori terrestrial ref- Galileo orbits with satellite attitude corrections measured erence frame. Sośnica et al. (2018) combined SLR meas- down to 1-s intervals for LEOs (Table 1). urements to Galileo, GLONASS, BeiDou and QZSS with We calculate the solutions based on LEOs-only, Gali- LAGEOS-1/2 and achieved an improvement of the SLR leo-only, and various LEOs, Galileo, and spherical geo- station coordinate repeatability w.r.t. LAGEOS-only solu- detic satellite combinations, also including diferent tions at the level of 6 to 15%, whereas in Sośnica et al. weighting of Normal Equation Systems (NEQs), and (2019) the authors achieved an improvement in terms diferent constraining of estimating parameters. In this of non-core SLR station coordinate repeatability from study, we assume the high accuracy of the GNSS-based about 20–30 mm to the level of 15–20 mm. Furthermore, orbits for the Galileo constellation provided as a part of the determination of Galileo orbits based solely on SLR the MGEX project, and for the LEOs determined by the observations can be found in Urschl et al. (2008), Hackel Astronomical Institute of the University of Bern (AIUB), et al. (2015), Bury et al. (2019). and by German Aerospace Center (Deutsches Zentrum für Luft- und Raumfahrt; DLR). Objectives of this study Te goal of this research is to derive station coordinates Methods based on SLR observations to eight active LEO satel- SLR normal points and data modeling lites: Sentinel-3A, GRACE-A/B, TerraSAR-X, Jason-2, Te ILRS provides time observations measured by SLR SWARM-A/B/C; 13 high-orbiting Galileo satellites (three stations in form of the normal points (NPs) in the con- IOV and ten FOC); and 3 passive spherical geodetic satel- solidated data format3. Te NPs are formed using dif- lites: LAGEOS-1/2 in medium orbits and LARES in a low ferent temporal size of data bin, which depend on the orbit. We aim to investigate SLR data to as large number mission type, and satellite orbit altitude, which, as shown of satellites as possible, especially in the case of LEOs for in Table 1, may vary from 5 to 300 s. Te modeling of SLR improving the determination of SLR station coordinates observations requires introducing various corrections. and to assess the consistency level between SLR obser- Corrections are related to signal propagation efects or vations collected to diferent missions. Te Sentinel-3A LRA models, such as: the general relativistic correction mission started on February, 2016, GRACE-A/B mission ended on October, 2017, and also other LEOs, such as SWARMs orbited the Earth in 2016. In addition, the 3 https://ilrs. gsfc. nasa. gov/ data_ and_ produ cts/ forma ts/ crd. html . Strugarek et al. Earth, Planets and Space (2021) 73:87 Page 5 of 21

due to the Earth gravitational bending of the light path at AIUB4 (orbit products: the ESA Copernicus Sentinel (Shapiro efect; Petit and Luzum 2010); the tropospheric Data Hub5), whereas the TerraSAR-X and Jason-2 orbits range correction for optical wavelength (Mendes and were provided by the DLR (Hackel et al. 2017). LEO Pavlis 2004); range biases which are station-specifc and orbits are generated in the 1-day solutions and are based satellite-specifc corrections; the LRA reference point on undiferentiated GPS phase measurements, the iono- correction, which considers the change of optical signal sphere-free linear combination of two frequencies L1 and propagation in the LRA prisms, and ofsets between LRA L2, using a reduced-dynamic approach (Wu et al. 1991) position to the satellite center-of-mass, and the center of with foat ambiguities and with applying the GPS antenna mass of trajectory obtained from the satellite orientation phase-center ofsets and variations (Jäggi et al. 2009). Te data and POD products. empirical accelerations were constrained using piecewise For spherical geodetic satellites, one center-of-mass constant parametrization and estimated in the radial, correction is sufcient to correct the measured range and along-track, and cross-track directions. Te non-gravita- refer it to the satellite center-of-mass. Tese corrections tional perturbing forces were accounted for by empirical are typically station-dependent because of the diferent accelerations without any a priori satellite macro-models. detector types and screening procedures employed at dif- Te LEO POD is analogous to that described in the study ferent SLR stations. For LEO satellites, two corrections by Arnold et al. (2019). are employed: one referring the center of LRA to the sat- In the case of the Galileo orbits, we use the 1-day orbits ellite center-of-mass and the second one which depends from the Center for Orbit Determination in Europe on the elevation and nadir angle of the laser incident (CODE) MGEX (Prange et al. 2018), which are based on angle. Tis allows for considering the specifc construc- network processing employing carrier phase double dif- tion of diferent LRA types consisting of diferent num- ferences, and the ionosphere-free linear combination of bers of corner cubes. For GNSS, fat LRAs are used with two frequencies E1 and E5a. For Galileo, the extended only one correction between the center of LRA and the empirical CODE orbit model ECOM2 (Arnold et al. center-of-mass of the satellites. For GNSS, the depend- 2015) is used assuming the yaw-steering attitude model encies between the elevation and nadir angle of the laser (Prange et al. 2017). incident angle are thus neglected, which directly maps In the case of both LAGEOS-1/2 and LARES, we gen- into the quality of registered SLR observations as the sat- erate 7-day orbit solutions with the estimation of the six ellite signature efect. Keplerian orbit parameters, fve empirical parameters, Te spacecraft attitude is irrelevant for POD and data i.e., constant acceleration and two periodic accelerations processing in the case of spherical geodetic satellites. in the along-track direction, two periodic accelerations However, for active LEO and GNSS satellites, informa- in the cross-track direction, and stochastic pulses in the tion about the spacecraft orientation is fundamental to along-track directions (Sośnica et al. 2018, 2019). We use properly refer the LRA position to the satellite center-of- the ILRS realization of the ITRF2014, SLRF2014, for sta- mass. Most of the GNSS satellites follow the yaw-steering tions, and the IGS14 for satellite microwave orbits (Rebi- mode, for which the spacecraft orientation and the LRA schung and Schmid 2016) as a priori station coordinate vector orientation can be calculated using the positions frames and the reference in station coordinate compari- of the Sun, Earth, and the satellite. Active LEO satel- sons. All three reference frame realizations: ITRF2014, lites follow diferent orientation modes, which can only IGS14, and SLRF2014 share the same origin, scale, and approximately be calculated using analytical formulas, the orientation and their rates over time, thus, are fully whereas the exact position has to be measured directly consistent. onboard satellites, using, e.g., star trackers and accelerometers. Orientation of the LEO spacecrafts is then SLR observations stored in the attitude fles and used for the calculation of Te screening of SLR measurements is performed for the LRA vector orientation with respect to the satellite each spherical geodetic solution, each LEO satellite- center-of-mass. only solution, and Galileo-only solution. Te screening is based on residuals between range observations and POD of satellites orbits. As a priori values, we use the IERS 14 C04 ERPs Precise orbits are needed for deriving the high-quality (Bizouard et al. 2019), and SLRF2014 for station coor- SLR station coordinates. In this study, the microwave dinates. We remove SLR observations with absolute data were used for POD of LEO and Galileo satellites, whereas the laser observations are used for POD of LAGEOS-1/2, and LARES satellites. Te Sentinel-3A, 4 http://ftp. aiub. unibe. ch/ . GRACE-A/B, SWARM-A/B/C orbits were generated 5 https://scihub. coper nicus. eu/ gnss/ . Strugarek et al. 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However, also other regions, such as South America and Africa, beneft in terms of the number of NPs. Moreo- ver, we investigate the distribution of SLR NPs in more local scale, i.e., for azimuth and zenith angles of NPs for the example three stations in the period of June 1–7, 2016 (Fig. 4). Te group of core stations, i.e., Yarragadee, Greenbelt, Matera, Hartebeesthoek, Haleakala, Zimmer- wald, Mt Stromlo, Graz, Herstmonceux, and Potsdam, which are considered as top-performing, are characterized by the largest number of NPs to LAGEOS satellites, in all directions [e.g., Yarragadee (7090) station, Fig. 4, left]. Furthermore, most of core stations provide a large number of NPs to LEOs, especially at high zenith angles, and a few NPs to Galileo. Monument Peak (7110) and Arequipa (7403) (Fig. 4) show few or no NPs to Galileo, Fig. 2 SLR observations to diferent types of satellites (LAR, LAG, LEO, a moderate number of NPs to LAGEOS or LARES satel- GAL) and sum of all (ALL) in 7-day batches lites, but relatively large number of NPs to LEO targets when compared to the core stations. Te NPs in 2016 to Galileo satellites constitute the lowest percentage of all residuals larger than 150 mm, or if the standard deviation collected NPs, and are generated, in the most of cases, of residuals is larger than 50 mm, the observations with based on observations collected at high elevation angles. largest residuals are being iteratively removed. Te reason for more NPs to Galileo at high elevation Figure 2 shows the number of SLR observations (NPs) angles is that the return link is much stronger thanks to to LARES (LAR), LEOs, Galileo (GAL), and LAGEOS-1/2 reduced atmospheric refraction and turbulences, lower (LAG) and the sum of all (ALL) in 7-day batches used in noise (during daytime), and closer satellite–station dis- the analysis after data screening. In total, 358,767 NPs tance. Te NPs to LEOs, are mostly collected at low are used for LEOs, 121,801 NPs for LAG, 73,551 NPs for elevation angles, due to the low probability of the satel- LARES, and 19,856 NPs for Galileo. Te sum of all obser- lite pass through the station zenith, and a short period of vations is 573,975. Te number of LEO observations is fyby above the SLR station. Tus, the LEO NPs should thus almost three times of that of LAGEOS NPs, whereas mostly infuence the horizontal components of station the Galileo constellation constitutes only 4% of all used coordinates, whereas the Galileo NPs should mostly NPs, which can be explained by difculties in tracking infuence the Up component of station coordinates, when high-orbiting satellites by ILRS stations. For GAL, the considering combined solutions based on SLR data to number of weekly SLR NPs is stable at the mean level of diferent satellites. 430 NPs, whereas for the LAR, LAG, and LEOs, we can observe an increase of the NPs number near the 115th Generation of NEQs and 225th day of the year, which may be explained by the After screening of SLR measurements, we generate the beginning of Sentinel-3A tracking in April 2016 and the NEQs for particular satellites. We use precise, daily, position of selected LEOs and spherical geodetic satel- microwave-based orbits of each LEO and Galileo, as well 6 lites on ILRS tracking priority list in 2016 . Including SLR as SLR-based 7-day orbits of LAGEOS-1/2 and LARES. data to LARES, Galileo, and in particular to LEOs, can Te generation of NEQs is based on linearized observa- increase the number of observations from the level of tion equations in the Gauss–Markof model with con- 2,400 NPs per week to the level of 11,500 NPs per week. sidering the diferences between SLR observations and Next, we investigate the global distribution of SLR NPs. modeled station–satellite ranges reduced by a series Figure 3 shows the global distribution of NPs collected by of corrections. We generate 1-day NEQs for each LEO SLR stations to LAG, all LEOs, Galileo and LARES satel- separately, 1-day NEQs for group of all used Galileo, lites used in this study for the example period of June 1–7, 7-day NEQs for both LAGEOS-1/2, and 7-day NEQs for 2016. Te number of NPs to other than LAG satellites LARES. NEQs include the parameters: station coordi- has increased in the Europe, Australia, and Asia regions. nates, range biases, GCC, the X and Y pole coordinates, and the Length of Day (LoD). In the case of all LEOs and Galileo, the orbital parameters in NEQs are fxed to the microwave-based orbits, whereas in the case of spherical 6 https://ilrs.cddis.eosdis.nasa.gov/missions/mission_operations/priorities/ geodetic satellites the orbit parameters are estimated. For history. html . Strugarek et al. Earth, Planets and Space (2021) 73:87 Page 7 of 21

satellite refector-specifc signature efects (Strugarek et al. 2019b), uncalibrated biases occurring in station device circuits (Otsubo et al. 2001; Sośnica et al. 2015b), or defciencies in SLR data modeling including the tropospheric delays (Drożdżewski et al. 2019). However, the estimation of range biases increases the number of parameters. Tus, to stabilize the solutions and to reduce the number of parameters, we calculate range biases in separate processing as mean values for the entire year and we introduce them to combined solutions as known quantities. Only the station coordinate corrections and annual average range biases for each SLR station to a particular satellite are estimated in the process of deriving annual biases. Annual range biases are treated as station-specifc, in analogy to Appleby et al. (2016), and satellite-specifc parameters. Te orbit parameters of spherical geodetic satellites are pre-elim- inated in the NEQs, whereas the ERPs, GCC, are fxed to a priori values to retrieve the range bias embedded in the SLR observations. In range bias processing, we use 1-day NEQs for LEOs, and Galileo data, and 7-day NEQs for LAGEOS-1/2 and LARES, all together to generate annual solutions referenced to the middle day of the year. We also tested diferent approaches, where annual range biases and station coordinates were calculated Fig. 3 Global distribution of SLR NPs collected by SLR stations for LAGEOS-1/2 satellites (top) and LAGEOS-1/2, LEO, Galileo, LARES using LAGEOS-1/2 only NEQs, then separately from satellites (bottom) from the period of June 1–7, 2016 LEO groups, and from Galileo NEQs, etc. However, these approaches resulted in cm-level biases for stations and a degradation of station coordinate results and thus are not shown here. LEO NEQs, we additionally introduce attitude orienta- Figure 5 shows the annual range biases for spherical tion fles with quaternions. We used information about geodetic, LEO, and Galileo satellites, calculated for each the characteristics of the LRA reference point7 and the 8 station–satellite pair. For Galileo satellites and most of center-of-mass corrections provided by the particular stations the range biases are negative within 10 to mission supplier that are distributed by the ILRS. Data − − 35 mm. For some stations, such as Komsomolsk (1868), screening and generation of NEQs were conducted using Arkhyz (1886), Katzively (1893) the annual range biases the modifed version of the Bernese GNSS Software reach over − 50 mm. Also Wettzell (8834), Monument (Dach et al. 2015). Peak (7110), Brasilia (7407), and Yarragadee (7090) show large range biases, up to − 40 mm to Galileo satellites. Range bias determination In the case of LEOs and the most of stations, the range Range biases constitute one of the major error sources biases are within ± 15 mm (Fig. 5). Te largest, negative when processing SLR data to LAGEOS (Drinkwater corrections are derived for Arkhyz (1886) and Katzively et al. 2007; Appleby et al. 2016), GNSS (Taller et al. (1893) station (up to − 50 mm), and also to Wettzell 2014; Sośnica et al. 2015b), or LEOs (Arnold et al. 2015; (8834) (up to − 30 mm). For some of the stations, e.g., Strugarek et al. 2019a). Te omission of introducing sta- Simeiz (1873), Altay (1879), and Arequipa (7403), range tion–satellite-specifc range bias may deteriorate the biases have large positive corrections at the level of solutions. Biases originate from erroneous sensor of- 30 mm. Spherical geodetic LARES and LAGEOS-1/2 sets, such as satellite center-of-mass corrections and satellites are characterized by the positive range biases at GNSS antenna ofset vectors, detector-specifc and the range of 5 to 15 mm for most of stations, with few

7 https://ilrs.cddis.eosdis.nasa.gov/missions/satellite_missions/current_missi ons/swma_ refe ctor. html , (an example for SWARM-A satellite) 8 https://ilrs.cddis.eosdis.nasa.gov/missions/spacecraft_parameters/center_ of_mass. html . Strugarek et al. Earth, Planets and Space (2021) 73:87 Page 8 of 21

Fig. 4 Distribution of SLR NPs for station azimuth and zenith angles to LAGEOS-1/2, LEO, Galileo, and LARES satellites from the period of June 1–7, 2016. An example for Yaragadee (7090, left), Monument Peak (7110, middle), Arequipa (7403, right) station

exceptions of large positive (40 mm) corrections, e.g., accounting for systematic errors, which lead to the more Altay (1879) or negative (even − 35 mm) corrections, e.g., accurate solutions. Katzively (1893), Wettzell (8834). Tendency towards positive range bias values for LAGEOS and LARES satellites Combined SLR solutions may be diminished by upgrading center-of-mass correc- Most of the parameters, i.e., SLR station coordinates, tions, as shown by Rodríguez et al. (2019). GCC, and ERPs are common in the Galileo, LEO, Te large annual range biases for Galileo are related LAGEOS, and LARES processing and can be stacked with POD products of satellites. In 2016, the CODE Gali- at the NEQ combination level. Te combined solu- leo orbits did not consider albedo, Earth infrared radia- tions require consistent models, including, e.g., models tion, and antenna thrust modeling, which in total result describing relativistic efects, gravity feld, solid Earth, in a shift of GNSS-derived satellite orbits of 36 to 40 mm ocean, and pole tides, and others. For the generation of in the radial direction (Bury et al. 2020). Te value of estimated range bias depends on antenna ofsets, phase ambiguity resolution, and POD product quality, and require a good SLR observation geometry to decorrelate station height and range bias estimates, which are calculated in annual processing as a mean annual value. Figure 6 shows the infuence of considering the annual range bias corrections by comparing the solutions with and without annual station–satellite range biases. We compare the interquartile range (IQR, that is the frst quartile subtracted from the third quartile) of coordinate residuals, derived as a diference of calculated SLR station coordinates to the SLRF2014 coordinates. In the case of the Up component, the reduction of IQR is 4 mm for LAGEOS, LEO, and Galileo solutions, whereas the North component is characterized by the reduction of IQR at the level of 2 mm for all tested solutions. Te East component is characterized by IQR reduction of 5, 3, 9 mm for the LAGEOS, LEOs, and Galileo solutions, respectively. Tus, introducing annual range biases is somewhat benefcial for processing SLR observations to Fig. 5 Annual average range biases for selected SLR station–satellite diferent types of satellites, and enhances the process of pairs in 2016 (E01–E30 names refer to Galileo PRNs). Gray area means no data Strugarek et al. Earth, Planets and Space (2021) 73:87 Page 9 of 21

described by Zajdel et al. (2019). After outlier detection, we updated the SLR core station list and recalculated the solutions. Individual and combined solutions were calculated using the modifed version of the Bernese GNSS software (Dach et al. 2015) for the period of 2016.0 to 2017.0. We test excluding some satellites (e.g., LEOs, LARES) from combinations or employing the weighting of NEQs in combined solutions to reduce the negative impact of the lowest-performing satellites. Excluding the satellites from combinations led to a decrease of the number of SLR observations and a decrease of the percentage of successful solutions for SLR stations, which resulted in Fig. 6 Repeatability of estimated station coordinates by the means no or rather minor improvement of determined parame- of IQR for LAGEOS (LAG), LEO satellites (LEO), and Galileo (GAL) with ters with respect to the LAGEOS solutions. Tus, we test and without introducing annual range bias correction (n/rb) combinations with NEQs weighting, in which weighting scale factors for the particular satellites are employed. Te scale factor can be expressed as ratio of the square NEQs, determination of annual range biases, processing roots of variances. In this study, we modify weighting of individual, and combined solutions, we use the same scale factors based on pre-analysis results. Te remain- models listed in Table 2. Te issue of possible reference ing processing scheme and estimated parameters are the frame diferences from SLRF2014 in SLR processing same as in the case of combined solutions, except for with IGS14 from LEO and Galileo orbits is discussed in NEQ weighting. the further part of article, that is ‘Network constraining To select weighting scale factors and investigate the tests’ section. Tests conducted by Strugarek et al. (2019a) quality of individual SLR solutions, we used the param- showed that 7-day LEO satellite solutions based on Sen- eter estimation approach. We analyze the estimated SLR tinel-3A/B are needed for a good and global distribution station coordinate repeatability by means of IQR 3D of SLR observing stations. Depending on the case study statistics of individual solutions based only on particu- (see Table 3), we generate LEO-only (LEO), Galileo-only lar LEO, LAGEOS-1/2, LARES, and 13 Galileo. Te 3D (GAL), LAGEOS-1/2-only (LAG), LARES-only (LAR) IQR value is calculated as a square root of the sum of the solutions and combinations, i.e., LEO+GAL, LAG+LAR, North, East, and Up IQRs squared. Figure 7 shows that LEO+GAL+LAG, ALL (all used satellites). Tus, an solutions based only on LAG, Sentinel-3A, Jason-2 are example of combined 7-day solution includes one 7-day characterized by the lowest 3D IQR of SLR station coor- NEQ for LAG, seven 1-day NEQs for Galileo, and seven dinates at the level of 21 mm. Te quality of LEO satel- 1-day NEQs of particular LEO satellites. lite orbits is better for the satellites at altitudes higher In the individual and combined solutions, we impose than 500 km (see Fig. 1, Table 1), due to the lower infu- no-net-rotation and the no-net-translation constraints ence of non-gravitational forces. Moreover, the shorter, for the SLR core station network group. Te core sta- 9 1 s attitude data intervals, were used in processing for tion list is provided by the ILRS Discontinuities File . Sentinel-3A, which may afect the particular LEO solu- We estimate SLR station coordinates, GCC, LoD, and tion (Table 1). However, the Jason-2 solution despite 30 s pole coordinates. Orbit parameters and annual range attitude interval is also characterized by low IQR 3D sta- biases are fxed to annual values. Station coordinates and tistics. Based on pre-analysis results (Fig. 7), we calcu- GCC are estimated as one set of parameters per 7-day lated the weighting scale factor for each satellite NEQs, solution. Te pole coordinates and the LoD parameter as a ratio between 3D IQR squared for LAGEOS to 3D are estimated with a 1-day resolution, parameterized IQR squared of particular satellite solution. Terefore, as piecewise linear (Table 2). For outlier detection of the weighting scheme resulted in scaling factors: 1.00 for core stations, the resulted coordinates of core stations LAG, Sentinel-3A, and Jason-2, 0.44 for SWARM-B/C, were verifed in every 7-day solution using a Helmert 0.25 for TerraSAR-X and Swarm-A, 0.16 for GRACE- transformation with imposing a threshold of 20 mm for A and LARES, and 0.11 for GRACE-B and Galileo. Te each coordinate component, which follows the strategy solutions based on weighted NEQs of all analyzed satellites are named ALL+W (Table 3).

9 https://ilrs.dgf.tum.de/fleadmin/data_handling/ILRS_Discontinuities_File. snx. Strugarek et al. Earth, Planets and Space (2021) 73:87 Page 10 of 21

Table 2 Models for Satellite Laser Ranging processing in individual and combined solutions Component Description

Estimated parameters Station coordinates, GCC, ERP Interval One set of parameters per 7 days (except for ERP with one set per day) Satellite positions From GPS-based POD for LEO, from CODE-MGEX for Galileo, from SLR- based POD for spherical satellites Center-of-mass position Provided by mission supplier and distributed by ILRS LRA reference point position Provided by mission supplier and distributed by ILRS Reference frame SLRF2014 [ILRS realization of ITRF2014, Altamimi et al. (2016)] Gravity feld EGM2008 (Pavlis et al. 2012) Solid Earth, pole, and ocean pole tides IERS2010 (Petit and Luzum 2010) Ocean tides FES2004 (Lyard et al. 2006) Ocean tidal loading FES2004 (calculated by Scherneck 1991) Tropospheric refraction IERS2010, Mendes and Pavlis (2004) Relativity IERS2010 (Petit and Luzum 2010) Software Bernese GNSS Software 5.2 (modifed version), Dach et al. (2015)

Table 3 List of tested solutions in the processing Case study name List of used satellites No. of satellites

LAG LAGEOS-1/2 2 LEOa Sentinel-3A, GRACE-A/B, Jason-2, TerraSAR-X, SWARM-A/B/C 8 LAR LARES 1 GAL Galileo 13 LEO GAL Sentinel-3A, GRACE-A/B, Jason-2, TerraSAR-X, SWARM-A/B/C, Galileo 21 + LAG LAR LAGEOS-1/2, LARES 3 + LEO GAL LAG Sentinel-3A, GRACE-A/B, Jason-2, TerraSAR-X, SWARM-A/B/C, Galileo, LAGEOS-1/2 23 + + ALL Sentinel-3A, GRACE-A/B, Jason-2, TerraSAR-X, SWARM-A/B/C, Galileo, LAGEOS-1/2, LARES 24 ALL W Sentinel-3A, GRACE-A/B, Jason-2, TerraSAR-X, SWARM-A/B/C, Galileo, LAGEOS-1/2, LARES weighting 24 + of NEQs constraining tests + + a Solutions for particular LEOs were derived separately

We tested also other weighing strategies based on coordinate residuals, and time series of station coordi- observation residuals and the a posteriori sigma of a unit nates. Finally, we conduct the tests with diferent con- weight of individual solutions, and standard deviations straining approaches to discuss the possible issue of of estimated station coordinates. However, the strategy reference frame inconsistencies. based on weights adjusted by using IQR values turned Figure 8 illustrates the SLR station coordinate IQR out to give the best results of the combinations out of all based on LAG, LEO, LAR, and GAL solutions. Con- tested strategies, therefore has been adopted for further sidering all stations, the lowest IQR values of the Up analyses. component are at the level of 17 mm for LAG and LEO solutions, whereas the East and North components are Results at the level of 10 and 11 mm for LAG and LEO, respec- Station network tively. Te LAR and GAL solutions are characterized We analyze calculated coordinates for all used SLR sta- by an IQR worse by a few to over a dozen mm in the tions, core stations, and the non-core group. First, we case of all components (Fig. 8, left). Considering the compare specifc satellite-type solutions, combinations core stations (Fig. 8, right), the lowest IQR values for of diferent satellite types, and the combinations with the Up component are at the level of 9–10 mm for LAG the weighting of observations in terms of IQR. Ten, we and LEO. Both horizontal components are at the low- investigate the formal errors of calculated station coor- est level of less than 5 and 7 mm of IQR for LAG and dinates, as well as number of solutions with improved LEO, respectively. LEO-only solutions obtain similar results w.r.t LAG solutions, the LAR solutions result Strugarek et al. Earth, Planets and Space (2021) 73:87 Page 11 of 21

in a few-mm worse results, whereas the GAL solutions In total 52 weekly solutions were generated in 2016.0– result in station coordinate statistics that are worse by a 2017.0. Numerous stations observe LAGEOS, LARES, dozen of mm. LEO and Galileo satellites on a regular basis, such as LAGEOS satellites allow for deriving high-quality sta- Yarragadee (7090), Changchun (7237), Mount Stromlo tion coordinates because of their mission characteris- (7825), or Greenbelt (7105). However, some stations, tics, such as orbit altitude, low area-to-mass ratio and such as Baikonur (1887), Komsomolsk (1868), Altay thus minimized orbit perturbing forces, and the homo- (1879), do not frequently observe LEO satellites, which geneous arrangement of corner cubes, which enables to is related with their main purpose to support GLO- compute an accurate correction for the satellite center- NASS, rather than tracking LEO targets, which have of-mass. Te LARES satellite has also low area-to-mass much shorter passes. Most of stations increased the per- ratio, but its orbital altitude, lower than that of LAGEOS, centage of obtained solutions, at the level of 10–20% for, makes LARES more sensitive to the residual atmospheric e.g., Monument Peak (7110), Wettzell (8834), Potsdam drag, time-variable geopotential changes and errors in (7841) or even doubled the percentage of solutions, such background models, such as ocean tidal model that are as Areqiupa (7403), Badary (1890), while comparing the not compensated by additional parameters, all of which ALL with LAG solutions. LEO targets caused the largest may generate orbit modeling errors and cause the infe- increase of possible solutions to obtain for stations in the rior quality of LAR solutions. Moreover, LAR solutions ALL approach. are based on measurements to only one satellite, which Figure 10 illustrates the repeatability of estimated sta- results in a decreased ratio of the number of observations tion coordinates by means of IQR for combined solu- to estimated parameters. However, we employ the same tions. When considering all stations (Fig. 10, left), IQR orbit modeling in terms of the number of empirical orbit values for the Up component are at level of 17, 16.5 mm parameters for LARES and LAGEOS-1/2 to keep a con- for LAG, and ALL+W, respectively, and at the level of sistency of both solutions and to investigate their impact 18 mm IQR for other tested solutions. Te horizontal on further combinations. components provide IQR values at the level of 9–10 mm, Te high-quality of SLR station coordinates based on for the ALL+W combinations. Te LAG solutions are altimetry LEO satellites at altitudes above 500 km (Sen- characterized by IQR values worse by 2 mm for the both, tinel-3A, Jason-2) confrms the high quality of microwave East and North components. When considering the LEO orbits. Microwave GNSS-based orbits beneft from: core stations (Fig. 10, right) and the Up component, IQR pseudo-stochastic accelerations, which absorb non-grav- results are less than 10 mm for ALL+W, and LAG, at the itational orbit perturbations and geopotential variations; level of 10–11 mm for remaining solutions. frequent attitude information data; high-quality LRA vec- Te results of IQR statistics for both ALL+W and LAG tors w.r.t. satellite center-of-mass; and satellite azimuth– are at a similar level with diferences of 0.5 mm, which is nadir-dependent range correction of the LRA reference less than a change of 5% in the case of all and core sta- point (Table 1). Galileo solutions are insufcient for the tions. Te horizontal components of non-core stations in determination of the highest-quality SLR station coordi- ALL+W show an improvement of 2-mm IQR, which cor- nates for the year 2016 due to the low number of observa- responds to 10% change, w.r.t LAG-only. Te LEO+GAL tions to single satellites, microwave orbit errors related to and LAG+LAR show the worst IQR values for all tested non-gravitational orbit perturbations (Bury et al. 2020). components and SLR station groups. Te improvement For Galileo, the LRA correction does not consider satel- of station repeatability for non-core stations might be lite azimuth–nadir angle corrections; therefore, the SLR caused by introducing a large number of SLR observa- observations at high-zenith angles are possibly afected tions, especially to high-quality LEO orbits. Te LEO tar- by errors for stations which are not designed to operate gets, characterized by precise microwave orbits, altitude at a low signal level from medium Earth orbit altitudes. higher than 500 km with frequent attitude information, Finally, Galileo satellites are typically observed only in have a positive impact on the combination results. Te the near-zenith direction, therefore the horizontal station LAG+LAR solutions are characterized by a deteriorated coordinates cannot be well determined as opposed to the IQR statistics, which suggests that LARES orbit modeling LEO satellites, for which the majority of observations are may require more frequent determination of dynamic collected at high zenith angles. orbit parameters than one set per 7-day to compensate Before the fnal combinations, we investigate the infu- for the residual atmospheric drag, time-variable gravity, ence of SLR data to other than spherical satellites. Fig- and errors in the background models. ure 9 shows how many station coordinates in % can be Te proper weighting of SLR data to other than spheri- successfully calculated from 7-day solutions for SLR cal geodetic satellite targets improves the quality of the stations when using LAG, LEO, and ALL observations. horizontal coordinate components for non-core stations. Strugarek et al. Earth, Planets and Space (2021) 73:87 Page 12 of 21

Core SLR station coordinates are neither improved nor (7838), Borowiec (7811), Arequipa (7403), Beijing (7249), deteriorated, however, the number of solutions increases. Katzively (1893). Some of the stations, such as Katzively Te determination of core station coordinates may be (1893), Arkhyz (1886), McDonald (7080), are character- improved when using more refned POD products, espe- ized by the coordinate statistics at the cm-level, which cially for LARES, Galileo, and LEOs at altitudes lower may be caused by a low number of SLR observations, or than 500 km. station-specifc errors. Te use of SLR measurements to other than spherical geodetic satellites increases precision for most of the non-core station coordinates for all SLR station coordinate quality components. Te core stations show neither a degrada- We check the observation geometry and the parameter tion nor a large improvement of the Up and horizontal observability for station coordinates in NEQs in terms components when compared to LAG results. Although, of station coordinate formal errors (Fig. 11). Te median introducing LEO, LARES, and Galileo SLR data can values of formal errors of all components are reduced for rather be treated as an enlargement of the number of ALL, and especially for ALL+W solutions, w.r.t. LAG observations, successful solutions, and the improvement solutions. While considering core stations, the median of observations geometry, which results in lower formal values of formal error for all components are less than errors of station coordinates, rather than the substitution 3 mm for LAG, and ALL solutions, and less than 1.5 mm of SLR data to LAGEOS. for ALL+W solutions. Also IQR values and the max– Next, we investigate whether the ALL+W combi- min ranges of formal errors of all components are about nations increase the number of solutions with lower 1–3 mm lower for ALL+W than for LAG solutions, e.g., coordinate residuals and reduce variability of coor- Hartebeesthoek (7501), Haleakala (7119), Graz (7839). In dinate time series w.r.t. the LAG solutions. Figure 12 the case of most of the non-core stations, median values shows two examples of stations: Potsdam and Areq- are higher by a few mm than for core stations, and vary uipa. For the Potsdam (7481) station, the number of from 1 to 5 mm, 1 to 7 mm, 1 to 6 mm, for the Up, North, solutions with residuals accumulated within the range and East components, respectively. Median values of − 4 to 4 mm for ALL+W is greater by 14, 10, and 8 non-core station formal errors show an improvement of than in LAG, for the Up, North, and East component, 0.5 and more than 1 mm for the Up and horizontal com- respectively (Fig. 12, left). In the case of Arequipa ponents, respectively, for ALL, ALL+W, w.r.t. the LAG (7403) (Fig. 12, right), ALL+W and LAG solutions solutions. Some of the stations, e.g., Arequipa (7403), are less concentrated around zero residual values than Borowiec (7811), Simeiz (1873), and Katzively (1893) for Potsdam (7841). However, ALL+W shows over 7, are characterized by an increased reduction of 3–4 mm 8, and 10 more solutions concentrated in the range of the median formal error for horizontal components, between − 4 and 4 mm than LAG, for the Up, North when comparing ALL+W with LAG solutions. A similar and East components, respectively. Thus, for Potsdam, reduction of a few mm occurs in terms of IQR, and max– and Arequipa there are even two times more ALL+W min range of formal errors for horizontal components. solutions with lower coordinate residuals than in LAG Almost all stations in ALL+W solution are character- solutions. Figure 13 shows an example of the Chang- ized by a substantial reduction of formal error statistics, chun (7237) station time series, decomposed into the w.r.t. LAG solutions. Te level of reduction is from 1 mm Up, North, and East components for LAG, ALL, and to even several mm, especially for horizontal compo- ALL+W solutions. In the case of the Up component, nents. Te reduction of station coordinate formal errors we can observe a 20 mm offset, which is related to is caused by the improvement of SLR observation geom- the inferior a priori station coordinates in SLRF2014 etry when introducing observations to satellites at dif- affected by a range bias and not fully valid non-linear ferent zenith angles (LEO for high angles and Galileo for post-seismic deformations after 2014. In the beginning low angles) with a good sky distribution as seen from the of 2016, all tested solutions show a variability of resid- SLR stations and the reduction of correlations between uals in the range of − 15 to 15 mm for all components. estimated parameters. The ALL and ALL+W solutions from April 2016 show A comparison of coordinate statistics for each SLR more stable results with variability in the range of less station (see Table 4) shows that in the case of most of than ±10 mm, in the case of the North and Up com- the stations, ALL+W solutions have IQR values lower ponents, when compared to LAG. LAG solution is by up to a few mm than the LAG solutions. Te reduc- affected by the larger variability and the larger formal tion of IQR occurs in the case of the core stations, e.g., errors than ALL and ALL+W. Hartebeesthoek (7501), Haleakala (7119), Matera (7941), Potsdam (7841), Arequipa (7403), and Changchun and especially for non-core stations, such as, Simosato (7237) constitute only some of the examples of stations Strugarek et al. Earth, Planets and Space (2021) 73:87 Page 13 of 21

Table 4 Median and interquartile ranges (IQR) of SLR station coordinates (in mm) CDP no. Station name LAG ALL W + Up North East Up North East

8834 Wettzell (WETL) 8.2 (9.5) 1.9 (8.3) 1.4 (9.5) 8.9 (9.6) 1.6 (8.1) 0.2 (6.7) − − − − − 7941 Matera (MATM) 6.6 (6.2) 2.0 (5.6) 1.5 (5.3) 7.4 (5.9) 2.2 (3.8) 1.0 (3.8) − − − − 7845 Grasse (GRSM) 0.4 (12.0) 0.1 (9.1) 0.4 (8.2) 0.1 (13.2) 0.7 (5.5) 2.1 (7.5) − − − − 7841 Potsdam (POT3) 5.6 (3.8) 1.0 (5.5) 0.0 (5.9) 2.3 (4.3) 0.7 (4.5) 0.7 (5.2) − − 7840 Herstmonceux (HERL) 9.7 (3.8) 0.6 (3.0) 1.0 (3.7) 9.3 (3.5) 0.2 (2.4) 0.1 (2.7) − − 7839 Graz (GRZL) 1.3 (3.8) 1.0 (4.1) 0.4 (3.7) 1.9 (3.6) 0.3 (2.9) 0.1 (4.1) − − − 7838 Simosato (SISL) 28.1 (9.0) 2.9 (9.1) 3.8 (8.1) 27.9 (6.6) 2.7 (7.3) 4.9 (6.3) − − − − 7827 Wettzell (SOSW) 12.6 (6.7) 9.2 (5.4) 2.6 (4.4) 12.9 (6.3) 9.9 (6.6) 1.6 (6.0) − − − − − − 7825 Mount Stromlo (STL3) 8.7 (4.2) 1.9 (2.9) 0.3 (4.0) 9.4 (4.3) 2.6 (2.4) 0.2 (3.0) − − 7821 Shanghai (SHA2) 8.6 (16.6) 3.9 (11.2) 1.1 (10.2) 9.9 (10.8) 3.3 (9.5) 1.4 (7.6) − 7811 Borowiec (BORL) 51.7 (46.7) 3.6 (49.7) 9.3 (57.9) 48.4 (23.8) 5.7 (13.4) 6.6 (11.0) − − 7810 Zimmerwald (ZIML) 2.7 (5.5) 0.3 (2.9) 0.6 (3.5) 1.1 (4.1) 0.8 (4.7) 0.8 (4.3) 7501 Hartebeesthoek (HARL) 3.9 (6.0) 1.5 (8.5) 1.6 (6.3) 2.6 (4.4) 3.6 (6.1) 3.1 (5.2) − − − 7407 Brasilia (BRAL) 5.3 (13.0) 62.4 (9.6) 27.0 (13.8) 6.0 (10.4) 64.5 (15.1) 26.6 (15.4) − − − − 7403 Arequipa (AREL) 3.5 (9.9) 1.7 (12.6) 0.7 (15.7) 2.7 (7.3) 2.9 (9.2) 3.9 (10.3) − − 7249 Beijing (BEIL) 19.2 (23.1) 5.3 (12.8) 2.7 (19.3) 17.4 (12.0) 6.1 (7.8) 1.0 (11.5) 7237 Changchun (CHAL) 25.8 (9.4) 4.2 (9.5) 0.1 (9.3) 25.7 (9.8) 2.0 (6.8) 1.0 (5.7) − − 7124 Tahiti (THTL) 12.6 (14.7) 2.2 (18.4) 0.3 (12.2) 12.0 (8.7) 2.5 (14.9) 3.4 (14.9) − − − 7119 Haleakala (HA4T) 7.5 (6.2) 2.9 (9.2) 3.5 (9.5) 5.0 (5.3) 3.3 (7.2) 3.0 (6.2) − − 7110 Monument Peak (MONL) 18.2 (5.2) 8.4 (6.8) 0.9 (9.3) 17.4 (4.8) 5.7 (9.8) 2.1 (8.5) − − − − − 7105 Greenbelt (GODL) 10.4 (5.7) 2.4 (3.5) 2.0 (6.6) 11.0 (5.0) 3.3 (3.5) 1.7 (3.4) − − 7090 Yarragadee (YARL) 4.9 (3.3) 0.7 (2.8) 0.0 (5.0) 6.2 (2.6) 1.3 (3.7) 0.4 (2.4) − − 7080 McDonald (MDOL) 28.6 (12.3) 6.6 (23.2) 7.8 (51.9) 9.8 (43.2) 16.2 (27.3) 3.6 (28.2) − − 1893 Katzively (KTZL) 57.3 (19.6) 10.7 (19.0) 3.4 (21.2) 57.2 (12.4) 12.2 (15.2) 2.5 (11.2) − − − − − − 1891 Irkutsk (IRKL) 3.1 (8.8) 18.4 (11.5) 17.1 (8.7) 7.9 (12.2) 15.9 (12.0) 16.6 (9.0) 1890 Badary (BADL) 3.6 (13.6) 14.0 (25.9) 5.8 (23.4) 4.8 (15.0) 0.4 (11.8) 4.2 (16.2) − − 1889 Zelenchukskaya (ZELL) 8.6 (9.1) 1.2 (13.4) 11.3 (12.6) 9.0 (9.1) 3.3 (19.8) 10.0 (13.3) − − − 1888 Svetloe (SVEL) 6.5 (8.7) 2.1 (16.4) 0.0 (15.9) 7.8 (9.0) 5.4 (12.2) 1.2 (12.1) − − − 1887 Baikonur (BAIL) 2.6 (18.7) 10.5 (12.1) 9.9 (9.1) 7.2 (17.2) 9.1 (18.6) 7.5 (19.1) − − 1886 Arkhyz (ARKL) 141.7 (11.8) 12.1 (18.4) 8.7 (14.5) 142.8 (9.8) 9.4 (12.5) 9.9 (17.1) − − − − 1879 Altay (ALTL) 43.1 (19.4) 5.2 (7.7) 4.4 (13.5) 42.1 (19.7) 6.9 (12.6) 6.8 (17.6) − − − − 1873 Simeiz (SIML) 5.5 (33.9) 41.6 (53.2) 0.6 (47.9) 5.3 (30.5) 15.1 (50.1) 11.0 (33.8) − 1868 Komsomolsk (KOML) 18.3 (26.4) 3.2 (20.5) 8.2 (17.4) 20.5 (27.4) 1.1 (20.5) 13.0 (14.7) − − − Bolded station numbers and location denote the core stations, IQR are given in parenthesis where adding SLR observations to diferent types of satel- of weighted combinations to investigate the infuence lites increases the number of solutions characterized by of fxed, microwave-based LEO and GNSS orbits on the lower residual values and reduces the variability of esti- realization of the reference frame. We generate com- mated coordinates. Station coordinates for other SLR bined solutions (ALL+W+NoPar) with no-net-rotation sites beneft in a similar way when considering multiple and no-net-translation network constraining, as in the SLR targets at various altitudes. case of ALL+W, LAG, and previous solutions. How- ever, remaining parameters, such as GCC and ERPs are Network constraining and SLR‑PPP solutions strongly constrained to a priori values or to values cal- Te combination of SLR observations to satellites, whose culated in the separate processing (annual range biases). orbits are calculated from SLR and GNSS techniques, ALL+W+NoPar should be characterized as very sta- implies the possibility of reference frame inconsistencies. ble solutions, because only station coordinates are We analyze diferent parameter constraining methods determined. Strugarek et al. Earth, Planets and Space (2021) 73:87 Page 14 of 21

In other tested combinations (ALL+W+PPP), we estimate SLR station coordinates as free parameters, with fxing all remaining parameters (except for LAG and LAR orbits). ALL+W+PPP solutions can be considered as SLR Precise Point Positioning (PPP) solutions in analogy to GNSS-PPP solutions, due to fxing microwave-based orbits and clocks, and not imposing any constraints on the station network. Te station coordinates are calculated independently for each station in PPP, because there are no common parameters that could establish the network solution. In SLR-PPP we do not need to estimate station clocks or troposphere delays as it is typically done in GNSS-PPP, because SLR measurement principle employs only one clock (the station clock), and modeling Fig. 7 Repeatability of estimated station coordinates by the means of troposphere delays in SLR is more accurate than in of IQR for LAGEOS, LARES, particular LEO satellite, and Galileo GNSS for the wet component of the atmosphere. We also constellation (pre-analysis results) tested SLR+PPP solutions based on SLR to LAGEOS-1/2

Fig. 8 Repeatability of estimated station coordinates by means of IQR from single satellite-type solutions for all SLR stations (left), and core SLR stations (right)

Fig. 9 The occurrence of SLR stations in 7-day solutions in the period 2016.0–2017.0 (expressed as percentage of possible to obtain 7-day station positions) Strugarek et al. Earth, Planets and Space (2021) 73:87 Page 15 of 21

Fig. 10 Repeatability of estimated station coordinates by means of IQR: all stations (left), non-core stations (middle), core stations (right)

Fig. 11 Station coordinate formal errors for LAG, ALL and ALL W solutions. Bolded station identifers denote the core stations. Box-plots include + median, 1st and 3rd quartile, maximum and minimum values

only (not shown), however the results of station coordi- and ALL+W+PPP solutions. ALL+W+NoPar solutions nates showed defciencies in the proper recovery of the are characterized by a similar repeatability of the Up and East station coordinate components. Large diferences of North components, w.r.t. LAG and ALL+W solutions. In the East station coordinate are caused by the singularity the case of the East component, the IQR are 3 mm higher of solution, due to unobservability of the ascending node for all tested groups of stations, w.r.t LAG and ALL+W. of LAGEOS orbits causing a singularity of the rotation of Nevertheless, the repeatability of estimated SLR station reference frame around Z-axis. Tis test showed that the coordinates does not substantially change when changing SLR-PPP solution is possible only on fxed orbits. the network constraining or when even estimating all sta- Figure 14 shows the repeatability of coordinates for the tion coordinates independently in SLR-PPP. group of all stations for LAG, ALL+W, ALL+W+NoPar, Strugarek et al. Earth, Planets and Space (2021) 73:87 Page 16 of 21

Fig. 12 Histogram of coordinate residuals, w.r.t SLRF2014, in LAG and ALL W solutions for Potsdam (7841) station (left) and Areqiupa (7403) station + (right)

because the origin is realized by the network of the stations. ALL+W+NoPar solutions characterized by the lowest number of estimated parameters show similar or worse by 3-mm results of station repeatability, which may be related to small inconsistencies in the reference frames and over-constraining of the solution. For ALL+W+PPP solutions, the realized frame is delivered by microwave orbits of LEO and GNSS in the IGS14 reference frame supported by SLR-based orbits of LAGEOS and LARES. Moreover, ALL+W+PPP solution results enforces the origin of the reference frame to be in the Earth’s center- of-mass because of no network constraining. Te reference frame origin in the PPP solutions is thus provided by the satellite orbits. Estimating stochastic parameters in the POD of LEOs allows them to orbit around the center-of-mass of the Earth. Te vector of center-of- mass referenced to the center-of-fgure represents the GCC. Tus, the relatively low 1–5 mm increase of IQR Fig. 13 Time series (with error bars) of station coordinate residuals in ALL W PPP solution is mostly caused by GCC for Changchun (7237) station for LAG, ALL, and ALL W solutions, + + + motion, and to a small extent by possible inconsistencies w.r.t. SLRF2014. Notice the change of residual range for Up component (top fgure) of reference frames delivered by diferent types of orbits. Moreover, introducing SLR measurements to other than LAGEOS satellites in SLR-PPP solutions removes the sin- gularities related to the drift of ascending node param- Network constraining in, e.g., LAG, ALL+W, eter, and allows for the determination of SLR station ALL+W+NoPar, enforces the determined reference coordinates. frame origin and orientation to those from the SLRF2014. To confrm this interpretation, we calculate the Te origin of the frame is then in the center-of-fgure Helmert transformation between ALL W and of the Earth or, more precisely, the center-of-network + ALL+W+NoPar solutions, and between ALL+W and Strugarek et al. Earth, Planets and Space (2021) 73:87 Page 17 of 21

Fig. 14 Repeatability of estimated station coordinates by means of IQR for diferent constraining tests

ALL+W+PPP solutions. Figure 15 shows the X, Y, and Z translation parameters compared with GCC estimated Fig. 15 Geocenter coordinates (GCC) from LAG and ALL W from ALL W and LAG solutions. Te X and Y GCC + + solutions compared to the translation parameters of Helmert show a high consistency of results, when comparing LAG transformation (HLM) calculated between ALL W and + with ALL W solutions. In the case of Z GCC, ALL W ALL W NoPar, and between ALL W and ALL W PPP solutions. + + + + + + + solutions are less scattered, but represent similar vari- We added 20 mm to the X geocenter and translation components ations as LAG solutions. Te X, Y, and Z translation and subtracted 20 mm from to the Z geocenter and translation components for visibility parameters of ALL+W and ALL+W+PPP show similar results to GCC from ALL+W and LAG, and confrm that station coordinates from ALL+W+PPP include the GCC motion. Tus, ALL+W solutions are not afected parameter constraining tests, and re-substitution of to a large extent by diferences between SLRF2014 and annual SLR range biases. IGS14 frames. Also, near-zero translation parameters of Te processing of SLR observations to diferent types ALL+W and ALL+W+NoPar solutions show that the of satellites for the estimation of parameters needs intro- infuence of the GCC motion is compensated by GCC ducing range bias corrections. Range biases are used that is estimated in ALL+W. for accounting of SLR systematic errors, which may be related to the orbit modeling, solution processing defciencies, delays in station circuits, troposphere refraction Conclusions and discussion biases, and others. We propose using the station–sat- Expansion of so far used SLR measurements to ellite-specifc annual range biases. Introducing annual LAGEOS-1/2 satellites, by considering also LARES, LEO, range bias correction increases the repeatability of sta- and Galileo data for the realization of the terrestrial ref- tion coordinates by 2 to 9 mm, depending on station erence frame and determination of station coordinates coordinate component and solution. In the case of LEO requires proper handling of range biases, high-quality satellites and most of stations, the annual the range biases satellite orbits, attitude information, and correct weight- are within the range of − 15 to + 15 mm, whereas for the ing of observations. In this study, we used SLR observa- Galileo satellites the annual range biases are within the tions from 33 laser stations to 24 satellites of diferent range of − 10 to even − 50 mm. characteristics, i.e., LAGEOS-1/2, LARES, Jason-2, Senti- SLR observations to spherical geodetic, LEO, and nel-3A, SWARM-A/B/C, TerraSAR-X, GRACE-A/B and Galileo satellites increased the number of used NPs by 13 Galileo to determine station coordinates based on the almost three times, and increased the percentage of methodology which combines laser data and microwave- successfully determined solutions for most of the SLR based orbits. Te processing considers GNSS-based stations, w.r.t. LAG-only solutions. Most of stations and SLR-based POD products of satellites, generating showed an increase of the number of combined solu- a series of 7-day solutions with no-net-rotation and no- tions at the level of 10–20%, w.r.t LAG-only solutions. net-translation network constraining, with verifcation Moreover, some stations, such as Arequipa or Badary, of the list of core stations, weighting tests, estimated even doubled the number of successfully determined station coordinates. Strugarek et al. Earth, Planets and Space (2021) 73:87 Page 18 of 21

Te determination of SLR station coordinates based on combination resulted in an improvement, especially for SLR data to LEO-only satellites results in an IQR at the horizontal coordinates of the non-core SLR stations, level of 17 mm for the Up component and 11 mm for the and no degradation of coordinates for the remaining horizontal components for all stations. For the core sta- stations. Findings correspond well with the research tions, the IQR is 10 mm for the Up, and 7 mm for the by Sośnica et al. (2014) based on the combination of horizontal components. Te IQR values of all stations for diferent types of spherical geodetic satellites, which multi-satellite combination are increased by about 2 mm also resulted in the most prominent improvement for the horizontal components, and at a similar level for the horizontal SLR station components. Also, the for the Up component, w.r.t LAG solutions. However, combinations results confrms the previous fndings the combined solution with weighting of observations of Strugarek et al. (2019b), where LAGEOS-1/2 and (ALL+W) does not deteriorate the statistics. Weight- Sentinel-3A/B combinations increased the consistency ing of observations is based on parameter estimation of station coordinates and allowed for the SLR-PPP approach in terms of station coordinate results for a par- approach. ticular satellite. Here, the IQR values of all stations from Te multi-satellite combination benefts the most ALL+W and LAG solutions are at the similar level of 17, from typically used spherical geodetic LAGEOS-1/2 10, and 9 mm for the Up, North, and East components, satellites, and two LEOs, i.e., Sentinel-3A, Jason-2, respectively. Te non-core SLR stations beneft the most characterized by the altitude higher than 500 km, the from the ALL+W approach. Te horizontal components high quality of attitude and spacecraft orientation of non-core stations show IQR lower by about 2-mm, information. However, the SLR data to the European which corresponds to the improvement of 10% w.r.t. LAG GNSS, Galileo, lead to inferior quality of station coordi- solutions. nates with respect to SLR tracking of LEO and spherical Also, the ALL+W solutions are characterized by bet- geodetic satellites. Te worse performance of Galileo ter statistics than LAG solutions in terms of geometry solutions is caused by a small number of observations of observations. Te reduction of the formal errors in in the analyzed period, microwave orbit errors, and the terms of median and IQR reaches even 50%, i.e., one to signature efect of fat LRA installed onboard GNSS, a few-mm level in the case of almost all stations. Te which increases the spread of measured ranges, when improvement of formal errors is largest for horizontal a satellite is observed at high zenith angles. Terefore, components. Te spread of coordinate residuals is also better modeling of the GNSS signature efect and nadir- better in the multi-satellite solutions which means that dependent corrections for GNSS LRAs are indispensa- the coordinate time series become more stable. Some ble for deriving high-quality geodetic parameters in the stations, such as Arequipa and Potsdam, have even two near future. LARES-only solutions also are of inferior times more solutions characterized by lower coordinate quality in terms of estimated station coordinates, due residuals in ALL+W than in LAG solutions, whereas to orbit quality, which require frequent determination the Changchun station shows more stable time series of of dynamic orbit parameters. coordinates that are reduced from about ± 15 to ± 10 Te study allowed for deriving the following highlights: mm. Moreover, combining SLR measurements to dif- ferent types of satellites allows for the determination of • Te vast majority of all SLR observations constitute SLR station coordinates without network constraining measurements to LEO satellites. When considering and independently for each station. Te SLR-PPP solu- them for other purposes than just the orbit valida- tions (ALL+W+PPP) show repeatability of all tested tion, i.e., determination of station coordinates, the station coordinates at the level of less than 20, 15, number of observations is increased, even by factor and 12 mm for the Up, East, and North components, of fve, the geometry of observations improves, and respectively. Te SLR-PPP solution has its origin the the formal errors of station coordinates are reduced. the Earth’s center-of-mass because the network origin • Te SLR–GNSS combination onboard LEO and Gal- is transferred by satellite orbits. ileo satellites allows for the inter-technique combina- Tis paper shows that SLR observations to spheri- tion through the co-location in space. cal geodetic, LEO and Galileo satellites together with • Mitigating of station–satellite-specifc range biases is precise microwave orbits of LEO and Galileo satellites, benefcial for the processing of SLR observations to allow for the determination of high-quality SLR sta- diferent types of satellites, as these parameters can tion coordinates. Te diferences of reference frames absorb systematic errors caused, e.g., by defcient delivered by SLR- and GNSS-based orbits in SLR com- orbit modeling. bination are minor and do not afect the solution. Te • Te solutions based on multi-satellite constellation of determination of station coordinates based on weighted geodetic, LEO, and GNSS satellites show a promising Strugarek et al. Earth, Planets and Space (2021) 73:87 Page 19 of 21

perspective for the estimation of SLR station coordi- improvement can likely be reached by using precise cor- nates. Te SLR-PPP solution is plausible when using rection of center-of-mass position for geodetic spherical multiple satellites. satellites (Rodríguez et al. 2019), ambiguity-fxed LEOs • Te multi-satellite combination with the proper orbits, with better consideration of orbit perturbations, weighting of observations shows better statistics such as non-gravitational force modeling and satellite of SLR station coordinates than the LAGEOS-only macromodels (Mao et al. 2020) or by using more precise solution. Te determined coordinates are character- Galileo orbits based on solutions which consider the box- ized by decreased formal errors, decreased variability wing model with the estimation of the small set of empir- of residuals and IQR values, and increased stability ical accelerations (Bury et al. 2020). Our approach can over time, especially for the non-core stations. How- also beneft from the modernization and the emergence ever, when the weighting is omitted, the estimated of other global GNSS systems, as well as the improve- parameters may be deteriorated with respect to the ment in SLR processing, such as range bias handling, LAGEOS-only solutions. upgrading models describing geopotential, time-variable gravity feld, atmosphere and ocean dealiasing, updating Methods of improving the quality of station coordinates center-of-mass correction, and modeling of satellite sig- and other parameters based on SLR technique consider nature efect and troposphere refraction biases. increasing the number SLR stations and their global Te approach described in this paper employs the distribution (e.g., Otsubo et al. 2016; Kehm et al. 2018; GNSS-based LEO orbits. Tus, the estimated parameters Glaser et al. 2019), or as in this study, exploiting the full of interest derived from the combination rely on observa- potential of SLR stations by using observations to vari- tions to spherical geodetic satellites, and consequently, to ous satellite types at diferent altitudes that are currently the performance of SLR technique. However, in the case being tracked by SLR stations. of observations to LEOs and Galileo, both SLR and GNSS Te processing in our approach requires consider- performance impact the combinations. As shown in our ing the features of two observation techniques, as well study, the quality of derived station coordinates confrms as specifc characteristics of observed satellites for the advancement in the consistency of SLR and GNSS as a determination of parameters. Te combined SLR data step towards the full integration of space geodetic tech- processing must employ: precise orbits of considered niques. Tis can be enhanced in the future by the simul- satellites, attitude information for LEOs, consistent refer- taneous POD of LEO using GNSS and SLR data and ence frames, compatible models describing phenomena co-location of both techniques onboard LEO satellites, of Earth’s and space systems, individual processing sce- which may diminish technique-specifc systematic errors narios for diferent types of satellites, and a reduction of and provide high-quality parameters. Nevertheless, this systematic efects, related to the observation techniques. paper shows a great potential and the excellent consist- Te quality of determined parameters may be limited due ency between GNSS-based LEO orbits, GNSS-based to time-variable number of satellites equipped with laser Galileo orbits, and SLR-based LAGEOS/LARES orbits in retrorefectors, sparse distribution of SLR stations, rela- the combined multi-GNSS satellite solutions, which is of tively low number of SLR observations, w.r.t GNSS, and crucial importance in terms of the GGOS goals aiming at the performance of SLR, and GNSS techniques. Recent the Earth monitoring with the accuracy of 1 mm. and ongoing developments conducted by various scientifc groups and space agencies led to improvement, e.g., Abbreviations in the terms of POD products, especially for LEOs (e.g., AIUB: Astronomical Institute of the University of Bern; DLR: German Aerospace CPOD Quality Working Group, Fernández et al. 2015) Center; DORIS: Doppler Orbitography and Radiopositioning Integrated by Sat- ellite; CDP: Crustal Dynamics Program; CODE: Center for Orbit Determination and GNSS satellites (e.g., MGEX project, Montenbruck in Europe; CPOD: Copernicus Precise Orbit Determination; ECOM2: Empirical et al. 2017), or upgrading processing models in spheri- CODE Orbit Model 2; ERP: Earth rotation parameter; ESA: European Space cal geodetic SLR satellites. Our expanded methodology Agency; FOC: Full Operational Capability; GCC: Geocenter coordinates; GGOS: Global Geodetic Observing System; GIOVE: Galileo In-Orbit Validation Element; may improve the realization of the SLR reference frame, GNSS: Global Navigation Satellite Systems; IAG: International Association of and therefore, should be taken into consideration in the Geodesy; ILRS: International Laser Ranging Service; IOV: In-Orbit Validation; further realizations of terrestrial reference frames. We ITRF: International Terrestrial Reference Frames; IQR: Interquartile ranges; LEO: Low Earth Orbiter; LoD: Length of day; LLR: Lunar Laser Ranging; MGEX: Multi- can expect a further improvement of results, based on GNSS Experiment; NEQ: Normal Equation Systems; NP: Normal point; POD: the derived approach when considering the development Precise orbit determination; RMS: Root-mean-square error; SLR: Satellite Laser of GNSS-based POD of LEOs and GNSS satellites and Ranging; VLBI: Very Long Baseline Interferometry. including other spherical geodetic satellites, e.g., Star- Acknowledgements lette, Stella, Ajisai or other observation techniques, such The International Laser Ranging Service is acknowledged for providing SLR as DORIS for the co-location in space onboard LEO. Te data (Pearlman et al. 2019a). The Center for Orbit Determination in Europe is Strugarek et al. Earth, Planets and Space (2021) 73:87 Page 20 of 21

acknowledged for the microwave Galileo orbits (Prange et al. 2018). The Astro- Bury G, Sośnica K, Zajdel R (2019) Multi-GNSS orbit determination using satel- nomical Institute of the University of Bern, the ESA Copernicus Sentinel Data lite laser ranging. J Geodesy 93(12):2447–2463. https://doi.org/10.1007/ Hub, and the German Aerospace Center, DLR are acknowledged for providing s00190-018-1143-1 the LEO orbit products. Bury G, Sośnica K, Zajdel R, Strugarek D (2020) Toward the 1-cm Galileo orbits: challenges in modeling of perturbing forces. J Geodesy 94(2):16. https:// Authors’ contributions doi.org/10.1007/s00190-020-01342-2 All the authors contributed to the design of the study. DS and KS came up Bury G, Sośnica K, Zajdel R, Strugarek D, Hugentobler U (2021) Determination with the idea of the study. DS carried out the experiments and drafted the of precise Galileo orbits using combined GNSS and SLR observations. GPS manuscript. All authors participated in the experimental analysis. All authors Solutions 25(1):11. https://doi.org/10.1007/s10291-020-01045-3 read and approved the fnal manuscript. Ciufolini I, Pavlis E, Chieppa F, Fernandes-Vieira E, Pérez-Mercader J (1998) Test of general relativity and measurement of the Lense-Thirring efect with Funding two earth satellites. Science 279(5359):2100–2103. https://doi.org/10. This work was supported by the OPUS Project from the National Science 1126/science.279.5359.2100 Center Poland under Contracts UMO-2019/35/B/ST10/00515. This research Ciufolini I, Paolozzi A, Pavlis EC, Koenig R, Ries J, Gurzadyan V, Matzner R, Pen- contributed to the initialization of the SPACE TIE project of the European rose R, Sindoni G, Paris C (2015) Preliminary orbital analysis of the LARES Research Council (grant agreement No. 817919). All views expressed are those space experiment. Eur Phys J Plus 130(7):133. https://doi.org/10.1140/ of the authors and not of the Agency. epjp/i2015-15133-2 Couhert A, Mercier F, Moyard J, Biancale R (2018) Systematic error mitigation in Availability of data and materials DORIS-derived geocenter motion. J Geophys Res Solid Earth 123(11):10– The SLR observations used for this study can be freely downloaded from the 142. https://doi.org/10.1029/2018JB015453 Crustal Dynamics Data Information System (Pearlman et al. 2019a; Noll et al. Dach R, Lutz S, Walser P, Fridez P (2015) Bernese GNSS software version 5.2. 2019) servers, i.e., ftp://cddis.nasa.gov/slr/products. Galileo orbits used for this user manual. University of Bern, Bern Open Publishing, Bern study can be downloaded from the Center for Orbit Determination (Prange Donlon C, Berruti B, Buongiorno A, Ferreira MH, Féménias P, Frerick J, Goryl et al. 2018) servers, i.e., http://ftp.aiub.unibe.ch/CODE_MGEX/. The other P, Klein U, Laur H, Mavrocordatos C, Nieke J, Rebhan H, Seitz B, Stroede datasets generated during and analyzed during the current study are available J, Sciarra R (2012) The Global Monitoring for Environment and Security from the corresponding author on reasonable request. (GMES) Sentinel-3 mission. Remote Sens Environ 120:37–57. https://doi. org/10.1016/j.rse.2011.07.024 Drinkwater MR, Haagmans R, Muzi D, Popescu A, Floberghagen R, Kern M, Declarations Fehringer M (2007) The GOCE gravity mission: ESA’s frst core explorer. In: Proceedings of the 3rd international GOCE user workshop, ESA special Competing interests publication, SP-627, ISBN 92-9092-938-3 The authors declare that they have no competing interests. Drożdżewski M, Sośnica K, Zus F, Balidakis K (2019) Troposphere delay modeling with horizontal gradients for satellite laser ranging. J Geodesy Author details 93(10):1853–1866. https://doi.org/10.1007/s00190-019-01287-1 1 Institute of Geodesy and Geoinformatics, Wrocław University of Environmen- 2 Fernández J, Escobar D, Peter H, Féménias P (2015) Copernicus POD service tal and Life Sciences, Grunwaldzka 53, 50‑357 Wrocław, Poland. Astronomical operations - orbital accuracy of Sentinel-1A and Sentinel-2A In: Proceed- Institute, University of Bern, Sidlerstrasse 5, 3012 Bern, Switzerland. ings of the international symposium space fight dynamics 19 Oct.-23 Oct. 2015. pp 1–14,Munich, Germany Received: 21 December 2020 Accepted: 10 March 2021 Friis-Christensen E, Lühr H, Knudsen D, Haagmans R (2008) Swarm—an earth observation mission investigating geospace. Adv Space Res 41(1):210– 216. https://doi.org/10.1016/j.asr.2006.10.008 Glaser S, König R, Neumayer KH, Balidakis K, Schuh H (2019) Future SLR station networks in the framework of simulated multi-technique terrestrial References reference frames. J Geodesy 93(11):2275–2291. https://doi.org/10.1007/ Altamimi Z, Rebischung P, Métivier L, Collilieux X (2016) ITRF2014: a new s00190-019-01256-8 release of the International Terrestrial Reference Frame modeling Gross R, Beutler G, Plag HP (2009) Integrated scientifc and societal user nonlinear station motions. J Geophys Rese Solid Earth 121(8):6109–6131. requirements and functional specifcations for the GGOS. In: Global geo- https://doi.org/10.1002/2016JB013098 detic observing system: meeting the requirements of a global society on Appleby G, Rodríguez J, Altamimi Z (2016) Assessment of the accuracy of a changing planet in 2020, Springer Berlin Heidelberg, Berlin, Heidelberg, global geodetic satellite laser ranging observations and estimated pp 209–224, https://doi.org/10.1007/978-3-642-02687-4_7 impact on ITRF scale: estimation of systematic errors in LAGEOS observa- Guo J, Wang Y, Shen Y, Liu X, Sun Y, Kong Q (2018) Estimation of SLR station tions 1993–2014. J Geodesy 90(12):1371–1388. https://doi.org/10.1007/ coordinates by means of SLR measurements to kinematic orbit of s00190-016-0929-2 LEO satellites. Earth Planets Space 70(1):201. https://doi.org/10.1186/ Arnold D, Meindl M, Beutler G, Dach R, Schaer S, Lutz S, Prange L, Sośnica K, s40623-018-0973-7 Mervart L, Jäggi A (2015) CODE’s new solar radiation pressure model for Hackel S, Steigenberger P, Hugentobler U, Uhlemann M, Montenbruck O GNSS orbit determination. J Geodesy 89(8):775–791. https://doi.org/10. (2015) Galileo orbit determination using combined GNSS and SLR 1007/s00190-015-0814-4 observations. GPS Solutions 19(1):15–25. https://doi.org/10.1007/ Arnold D, Montenbruck O, Hackel S, Sośnica K (2019) Satellite laser ranging to s10291-013-0361-5 low Earth orbiters: orbit and network validation. J Geodesy 93(11):2315– Hackel S, Montenbruck O, Steigenberger P, Balss U, Gisinger C, Eineder M 2334. https://doi.org/10.1007/s00190-018-1140-4 (2017) Model improvements and validation of TerraSAR-X precise orbit Bizouard C, Lambert S, Gattano C, Becker O, Richard JY (2019) The IERS determination. J Geodesy 91(5):547–562. https://doi.org/10.1007/ EOP 14C04 solution for Earth orientation parameters consistent s00190-016-0982-x with ITRF 2014. J Geodesy 93(5):621–633. https://doi.org/10.1007/ Haines BJ, Bar-Sever YE, Bertiger WI, Desai SD, Harvey N, Sibois AE, Weiss JP s00190-018-1186-3 (2015) Realizing a terrestrial reference frame using the Global Positioning Bloßfeld M, Müller H, Gerstl M, Štefka V, Bouman J, Göttl F, Horwath M (2015) System. J Geophys Res Solid Earth 120(8):5911–5939. https://doi.org/10. Second-degree Stokes coefcients from multi-satellite SLR. J Geodesy 1002/2015JB012225 89(9):857–871. https://doi.org/10.1007/s00190-015-0819-z Hofmann F, Biskupek L, Müller J (2018) Contributions to reference systems Buckreuss S, Balzer W, Muhlbauer P, Werninghaus R, Pitz W (2003) The terraSAR- from Lunar Laser Ranging using the IfE analysis model. J Geodesy X satellite project. In: IGARSS 2003. 2003 IEEE international geoscience 92(9):975–987. https://doi.org/10.1007/s00190-018-1109-3 and remote sensing symposium. Proceedings (IEEE Cat. No.03CH37477), Jäggi A, Dach R, Montenbruck O, Hugentobler U, Bock H, Beutler G (2009) vol 5, pp 3096–3098. https://doi.org/10.1109/IGARSS.2003.1294694 Phase center modeling for LEO GPS receiver antennas and its impact on Strugarek et al. Earth, Planets and Space (2021) 73:87 Page 21 of 21

precise orbit determination. J Geodesy 83(12):1145. https://doi.org/10. Rebischung P, Schmid R (2016) IGS14/igs14.atx: a new Framework for the IGS 1007/s00190-009-0333-2 Products. AGU fall meeting abstracts 2016:G41A-0998 Johnston G, Riddell A, Hausler G (2017) The International GNSS service. Reigber C, Lühr H, Schwintzer P (2000) Status of the CHAMP mission. In: Springer International Publishing, Cham, pp 967–982. https://doi.org/10. Rummel Reinhard, Drewes H, Wolfgang B, Helmut H (eds) Towards an 1007/978-3-319-42928-1_33 integrated global geodetic observing system (IGGOS). Springer, Berlin, Kehm A, Bloßfeld M, Pavlis EC, Seitz F (2018) Future global SLR network pp 63–65 evolution and its impact on the terrestrial reference frame. J Geodesy Rodríguez J, Appleby G, Otsubo T (2019) Upgraded modelling for the determi- 92(6):625–635. https://doi.org/10.1007/s00190-017-1083-1 nation of centre of mass corrections of geodetic SLR satellites: impact on Koenig D (2018) A Terrestrial Reference Frame realised on the observation key parameters of the terrestrial reference frame. J Geodesy 93(12):2553– level using a GPS-LEO satellite constellation. J Geodesy 92(11):1299–1312. 2568. https://doi.org/10.1007/s00190-019-01315-0 https://doi.org/10.1007/s00190-018-1121-7 Scherneck HG (1991) A parametrized solid earth tide model and ocean tide Krieger G, Moreira A, Fiedler H, Hajnsek I, Werner M, Younis M, Zink M (2007) loading efects for global geodetic baseline measurements. Geophys J Int TanDEM-X: a satellite formation for high-resolution SAR interferometry. 106(3):677–694. https://doi.org/10.1111/j.1365-246X.1991.tb06339.x IEEE Trans Geosci Remote Sens 45(11):3317–3341. https://doi.org/10. Schlüter W, Behrend D (2007) The International VLBI Service for Geodesy and 1109/TGRS.2007.900693 Astrometry (IVS): current capabilities and future prospects. J Geodesy Lambin J, Morrow R, Fu LL, Willis JK, Bonekamp H, Lillibridge J, Perbos J, 81(6):379–387. https://doi.org/10.1007/s00190-006-0131-z Zaouche G, Vaze P, Bannoura W, Parisot F, Thouvenot E, Coutin-Faye S, Sośnica K, Jäggi A, Thaller D, Beutler G, Dach R (2014) Contribution of Starlette, Lindstrom E, Mignogno M (2010) The OSTM/Jason-2 mission. Marine Stella, and AJISAI to the SLR-derived global reference frame. J Geodesy Geodesy 33(sup1):4–25. https://doi.org/10.1080/01490419.2010.491030 88(8):789–804. https://doi.org/10.1007/s00190-014-0722-z Lyard F, Lefevre F, Letellier T, Francis O (2006) Modelling the global ocean tides: Sośnica K, Jäggi A, Meyer U, Thaller D, Beutler G, Arnold D, Dach R (2015a) Time modern insights from FES2004. Ocean Dyn 56(5):394–415. https://doi. variable Earth’s gravity feld from SLR satellites. J Geodesy 89(10):945–960. org/10.1007/s10236-006-0086-x https://doi.org/10.1007/s00190-015-0825-1 Mao X, Arnold D, Girardin V, Villiger A, Jäggi A (2020) Dynamic GPS-based Sośnica K, Thaller D, Dach R, Steigenberger P, Beutler G, Arnold D, Jäggi LEO orbit determination with 1 cm precision using the Bernese GNSS A (2015b) Satellite laser ranging to GPS and GLONASS. J Geodesy Software. Advances in space research. https://doi.org/10.1016/j.asr.2020. 89(7):725–743. https://doi.org/10.1007/s00190-015-0810-8 10.012, URL http://www.sciencedirect.com/science/article/pii/S0273 Sośnica K, Bury G, Zajdel R (2018) Contribution of multi-GNSS constellation 117720307237 to SLR-derived terrestrial reference frame. Geophys Res Lett 45(5):2339– Männel B, Rothacher M (2017) Geocenter variations derived from a combined 2348. https://doi.org/10.1002/2017GL076850 processing of LEO- and ground-based GPS observations. J Geodesy Sośnica K, Bury G, Zajdel R, Strugarek D, Drozdzewski M, Kaźmierski K (2019) 91(8):933–944. https://doi.org/10.1007/s00190-017-0997-y Estimating global geodetic parameters using SLR observations to Galileo, Mendes VB, Pavlis EC (2004) High-accuracy zenith delay prediction at optical GLONASS, BeiDou, GPS, and QZSS. Earth Planets Space 71(1):20. https:// wavelengths. Geophys Res Lett. https://doi.org/10.1029/2004GL020308 doi.org/10.1186/s40623-019-1000-3 Montenbruck O, Steigenberger P, Prange L, Deng Z, Zhao Q, Perosanz F, Steigenberger P, Montenbruck O (2017) Galileo status: orbits, clocks, and Romero I, Noll C, Stürze A, Weber G, Schmid R, MacLeod K, Schaer S positioning. GPS Solutions 21(2):319–331. https://doi.org/10.1007/ (2017) The multi-GNSS experiment (MGEX) of the International GNSS s10291-016-0566-5 Service (IGS)—achievements, prospects and challenges. Adv Space Res Strugarek D, Sośnica K, Arnold D, Jäggi A, Zajdel R, Bury G, Drozdzewski M 59(7):1671–1697. https://doi.org/10.1016/j.asr.2017.01.011 (2019a) Determination of global geodetic parameters using Satellite Noll CE, Ricklefs R, Horvath J, Mueller H, Schwatke C, Torrence M (2019) Laser Ranging measurements to Sentinel-3 satellites. Remote Sens. Information resources supporting scientifc research for the International https://doi.org/10.3390/rs11192282 Laser Ranging Service. J Geodesy 93(11):2211–2225. https://doi.org/10. Strugarek D, Sośnica K, Jäggi (2019b) Characteristics of GOCE orbits based on 1007/s00190-018-1207-2 Satellite Laser Ranging. Adv Space Res 63(1):417–431. https://doi.org/10. Otsubo T, Appleby GM, Gibbs P (2001) Glonass laser ranging accuracy with 1016/j.asr.2018.08.033 satellite signature efect. Surv Geophys 22(5):509–516. https://doi.org/10. Tapley BD, Bettadpur S, Watkins M, Reigber C (2004) The gravity recovery and 1023/A:1015676419548 climate experiment: mission overview and early results. Geophys Res Lett. Otsubo T, Matsuo K, Aoyama Y, Yamamoto K, Hobiger T, Kubo-oka T et al (2016) https://doi.org/10.1029/2004GL019920 Efective expansion of satellite laser ranging network to improve global Thaller D, Dach R, Seitz M, Beutler G, Mareyen M, Richter B (2011) Combination geodetic parameters. Earth,Planets Space 68(1):65. https://doi.org/10. of GNSS and SLR observations using satellite co-locations. J Geodesy 1186/s40623-016-0447-8 85(5):257–272. https://doi.org/10.1007/s00190-010-0433-z Pavlis NK, Holmes SA, Kenyon SC, Factor JK (2012) The development and Thaller D, Sośnica K, Steigenberger P, Roggenbuck O, Dach R (2014) Pre- evaluation of the Earth Gravitational Model 2008 (EGM2008). J Geophys combined GNSS-SLR solutions: what could be the beneft for the ITRF? Res Solid. https://doi.org/10.1029/2011JB008916 In: van Dam T (ed) REFAG 2014. Springer International Publishing, Cham, Pearlman MR, Noll CE, Pavlis EC, Lemoine FG, Combrink L, Degnan JJ, Kirchner pp 85–94 G, Schreiber U (2019a) The ILRS: approaching 20 years and planning for Urschl C, Beutler G, Gurtner W, Hugentobler U, Ploner M (2008) Orbit deter- the future. J Geodesy 93(11):2161–2180 mination for GIOVE-a using SLR tracking data. In: 15th international Pearlman M, Arnold D, Davis M, Barlier F, Biancale R, Vasiliev V, Ciufolini I, workshop laser ranging, Canberra, pp 40–46 Paolozzi A, Pavlis EC, Sośnica K, Bloßfeld M (2019b) Laser geodetic satel- Willis P, Fagard H, Ferrage P, Lemoine FG, Noll CE, Noomen R, Otten M, Ries JC, lites: a high-accuracy scientifc tool. J Geodesy 93(11):2181–2194. https:// Rothacher M, Soudarin L, Tavernier G, Valette JJ (2010) The International doi.org/10.1007/s00190-019-01228-y DORIS Service (IDS): toward maturity. Adv Space Res 45(12):1408–1420. Petit G, Luzum B (2010) IERS conventions (2010) IERS technical note 36. Verlag https://doi.org/10.1016/j.asr.2009.11.018 des Bundesamts für Kartographie und Geodäsie, Frankfurt am Main, p Wu SC, Yunck TP, Thornton CL (1991) Reduced-dynamic technique for precise 179 orbit determination of low earth satellites. J Guidance Control Dyn Plag HP, Pearlman M (2009) Global geodetic observing system: meeting the 14(1):24–30. https://doi.org/10.2514/3.20600 requirements of a global society on a changing planet in 2020. Springer, Zajdel R, Sośnica K, Drożdżewski M, Bury G, Strugarek D (2019) Impact of Berlin network constraining on the terrestrial reference frame realization based Prange L, Orliac E, Dach R, Arnold D, Beutler G, Schaer S, Jäggi A (2017) on SLR observations to LAGEOS. J Geodesy 93(11):2293–2313. https://doi. CODE’s fve-system orbit and clock solution-the challenges of multi- org/10.1007/s00190-019-01307-0 GNSS data analysis. J Geodesy 91(4):345–360. https://doi.org/10.1007/ s00190-016-0968-8 Prange L, Arnold D, Dach R, Schaer S, Sidorov D, Stebler P, Villiger A, Jäggi A Publisher’s Note (2018). CODE product series for the IGS MGEX project. https://boris.unibe. Springer Nature remains neutral with regard to jurisdictional claims in pub- ch/id/eprint/75882 lished maps and institutional afliations.